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tap rule

ok, more info.

Nothing yet exists.
There is a main ( I don't know what athe ampacity is) So from what Info I could gather one panel is going to be 225 amps and then the other is going to be tapped off of the first one also at 225 amps. I think we would go with 4/0, (foreman says 3/0) from the main and then the tap would have what size wire? the same?
Could someone exlain what "the rating of the oc device on the line side of the tap conductors shall not exceed 10 times the ampacity of the tap conductor" mean...?does it mean that whatever we tap off the 225 needs to be 22.5 amps or larger?

OK, I am still confused. Let’s start here: You say that nothing yet exists, but I infer that there does exist some upstream panel that will be feeding the two new panels you have been discussing. Within that upstream panel, there will be a breaker that will serve the first of your two new panels. What is that breaker’s rating? Next, what is the ampacity of the wire from that breaker to the first panel? If I were designing this setup, my answers to those two questions would be, 225 amps, and 4/0, in that order.

Part of my confusion is that I think you are using the word “tap” as though it meant the same thing as “connect a wire to.” It does not. Rather, it means something like "connect a smaller wire to a bigger wire." Specifically, when you connect a new wire to an existing wire, you only call it a “tap” if the ampacity of the second wire is lower than the trip rating of the breaker that is protecting the first wire. In other words, if in your situation you have a 225 amp breaker that is protecting a 4/0 wire that serves the first 225 amp panel, and if you connect another 4/0 wire from the first panel to the second panel, then you do not have a “tap” situation. The second wire would be adequately protected by the 225 amp breaker.

Now, if you wanted to use a smaller wire than 4/0 from the first panel to the second panel, that smaller wire would not be adequately protected by the upstream 225 amp breaker. You are allowed to do that if you follow the tap rules in 240.21. But you are feeding a 225 amp panel, so why would you want to feed it with a wire that does not have the full 225 amp ampacity?

The foreman is wrong. That is, unless the foreman can produce a calculation that shows that the load is no higher than 200 amps (i.e., the ampacity of a 3/0), then you need a 4/0 to serve the 225 amp panel.